Probability Examples

Probability is a numerical measure which indicates the chance of occurrence. For example: when a die is rolled you may get any outcome like 1, 2, 3, 4, 5 or 6.There are three different type of approaches used in probability namely:1) Classical approach2) Empirical approach3) The Axiomatic approach. These three approaches have their own advantages and disadvantages. In this page you will learn to solve different types of problems in probability.

The conditional probability of an event will occur when another event is already occurred. Below are some problems on conditional probability.

Example 1: A box contains 7 white and 3 pink balls. Three balls are drawn at random from the box. Find the probability that both of them are white when,1) Drawn without replacement.2) Drawn with replacement.

Solution :1)Drawn without replacement.The balls are drawn one after the other. The balls drawn are not returned to the box in this case.Let $A$ : First ball drawn is White. $B$ : Second ball drawn is White.

$P(A)$ = $\frac{7}{10}$

$P$ $(\frac{B}{A})$ = $\frac{6}{9}$ = $\frac{2}{3}$, because when A has happened, the box will have only 6 white and 3 pink balls.

Therefore, $P$ [Both the balls are white] = $P(A \cap B)$

= $P(A)$ . $P$ $(\frac{B}{A})$

= $\frac{7}{10}$ $\times$ $\frac{2}{3}$

= $\frac{14}{30}$

= 0.47

2)Draw with replacement.The balls are drawn one after the other. However after drawing the first ball, the drawn ball is returned to the bag before the second draw is made.Let $A$ : First ball drawn is White. $B$ : Second ball drawn is White.

$P(A)$ = $\frac{7}{10}$Contents of the bag remain unaltered as the first ball drawn is returned before the second draw.

Therefore, $P$ [Both the balls are White] = $P(A \cap B)$

= $P(A)$ . $P$($\frac{B}{A}$)

= $\frac{7}{10}$ $\times$ $\frac{7}{10}$

= $\frac{49}{100}$

= 0.49

Example 2: A van has 15 packets of mangoes, among them 7 packets are Alphonso and 8 packets are kesar.1) Find the probability of getting Kesar?2) Find the probability of getting Alphonso?3) Find the probability of getting Alphonso and then Kesar?

Solution :Given:A van has 15 packets of mangoes. 7 packets are Alphonso and 8 packets are kesar.1) Probability of getting Kesar.As there are 8 kesar packets of mangoes among 15,

Probability of getting a kesar packet will be $\frac{8}{15}$

2) Probability of getting Alphonso.As there are 7 packets of Alphonso among 15,